André-Marie Ampère

André-Marie Ampere

André-Marie Ampère (1775-1836), was a French physicist, natural philosopher, and mathematician who is best known for his important contributions to the study of electrodynamics. He invented the astatic needle, a critical component of the modern astatis galvanometer, and was the first to demonstrate that a magnetic field is generated when two parallel wires are charged with electricity. He is generally credited as one of the first to discover electromagnetism. Born January 20, 1775, Ampère was the son of a successful businessman and local government official in Polemieux-auMont-d'Or, a small community near Lyon, France. As a child Ampere spent a great deal of time reading in the library of his family home, and he voraciously consumed books of history, geography, literature, philosophy and the natural sciences. His father taught him Latin and encouraged Ampère to pursue his passion for mathematics. Some historians write that the young Ampère was a math prodigy at a very early age and that he used to work out long mathematical formulas, just for his own personal entertainment, using small pebbles or breadcrumbs to represent groups of numbers.

Even without any formal education Ampère began a career as a science teacher. After teaching for a while in Lyon he accepted positions at institutions of higher learning including the College of France and the Polytechnic School at Paris, where he was a professor of mathematics. It was there that he first conducted important research and experiments into the nature of electrical and magnetic forces. In the early 1820s, after learning about the electromagnetism experiments of Hans Christian Oersted, Ampère began to formulate a combined theory of electricity and magnetism, doing several demonstrations involving magnetic and electrical forces. His work confirmed and validated the discoveries of Oersted while also expanding upon them, helping to accelerate work in the field of electromagnetism around the world.

Ampère's most significant scholarly paper on the subject of electricity and magnetism, titled Memoir on the Mathematical Theory of Electrodynamic Phenomena, was published in 1826. The theoretical foundation presented in this publication served as the basis for other ideas of the 19th century regarding electricity and magnetism. It helped to inspire research and discoveries by scientists including Faraday, Weber, Thomson, and Maxwell.

Ampère was elected to the prestigious National Institute of Sciences in 1814, and was awarded a chair at the University of France in 1826. There he taught electrodynamics and remained a member of the faculty until his death. He was also a member of the Fellows of the Royal Society of London

Despite his celebrated accomplishments, Ampere led a rather tragic life. When Lyons was taken over by rebels during the French Revolution, his beloved father was a district judge. Because of his political affiliations, Ampère’s father was taken as a political prisoner and then publicly executed by guillotine, an event that severely scarred the young Ampère and led to a period of psychological depression. Later in life Ampère’s first wife met with an early death after a prolonged illness, and although he remarried, his second marriage was unhappy and unsuccessful.

Ampère died June 10, 1836 in Marseilles, France, and was buried in the Montmartre Cemetery in Paris. When Gustave Eiffel built his famous Eiffel Tower in Pairs in 1889, he included the names of 72 prominent French scientists on plaques around the first section at the base of the structure. The name of André-Marie Ampère is included in that distinguished memorial.

The ampere – the unit for measuring electric current – was named in honor of Ampère. In the past, an ampere was understood as the force generated between parallel electrically charged wires, but as scientific knowledge evolves over time, the definition of “ampere” sometimes changes slightly also. The current modern definition of ampere describes the ability of a specified current to deposit a precise amount of a substance on an electrode during electrolysis.

Charles Augustin Coulomb

Charles Augustin Coulomb

Born: 14 June 1736 in Angoulême, France
Died: 23 Aug 1806 in Paris, France

Charles Augustin Coulomb's father was Henry Coulomb and his mother was Catherine Bajet. Both his parents came from families which were well known in their fields. His father's family were important in the legal profession and in the administration of the Languedoc region of France, and his mother's family were also quite wealthy. After being brought up in Angoulême, the capital of Angoumois in southwestern France, Coulomb's family moved to Paris. In Paris he entered the Collège Mazarin, where he received a good classical grounding in language, literature, and philosophy, and he received the best available teaching in mathematics, astronomy, chemistry and botany.


At this stage in his education there was a crisis for Coulomb. Despite his father's good standing, he had made unsuccessful financial speculations, had lost all his money and moved from Paris to Montpellier. Coulomb's mother remained in Paris but Coulomb had a disagreement with her over the direction his career should take so he left Paris and went to Montpellier to live with his father. At this stage Coulomb's interests were mainly in mathematics and astronomy and while in Montpellier he joined the Society of Sciences there in March 1757 and read several papers on these topics to the Society.


Coulomb wanted to enter the École du Génie at Mézières but realised that to succeed in passing the entrance examinations he needed to be tutored. In October 1758 he went to Paris to receive the tutoring necessary to take the examinations. Camus had been appointed as examiner for artillery schools in 1755 and it was his Cours de mathématiques that Coulomb studied for several months. In 1758 Coulomb took the examinations set by Camus which he passed and he entered the École du Génie at Mézières in February 1760. He formed a number of important friendships around this time which were important in his later scientific work, one with Bossut who was his teacher at Mézières and the other with Borda.


Coulomb graduated in November 1761. He was now a trained engineer with the rank of lieutenant in the Corps du Génie. Over the next twenty years he was posted to a variety of different places where he was involved in engineering, in structural design, fortifications, soil mechanics, and many other areas. His first posting was to Brest but in February 1764 he was set to Martinique in the West Indies. Martinique fell under the sovereignty of France under Louis XIV in 1658. However Martinique was attacked by a number of foreign fleets over the following years. The Dutch attacked it in 1674 but were driven off, as were the English in 1693 and the English again in 1759. Martinique was finally captured by the English in 1762 but were returned to France under the terms of the Treaty of Paris in 1763. The French then made attempts to make the island more secure by building a new fort.


Coulomb was put in charge of the building of the new Fort Bourbon and this task occupied him until June 1772. It was a period during which he showed the practical side of his engineering skills which were needed to organise the construction, but his experiences would play a major role in the later theoretical memoirs he wrote on mechanics. As far as Coulomb's health was concerned these were difficult years and the illnesses which he suffered while on Martinique left him in poor health for the rest of his life.


On his return to France, Coulomb was sent to Bouchain. However, he now began to write important works on applied mechanics and he presented his first work to the Académie des Sciences in Paris in 1773. This work, Sur une application des règles, de maximis et minimis à quelque problèmes de statique, relatifs à l'architecture was written (in Coulomb's words, see for example ):-


... to determine, as far as a combination of mathematics and physics will permit, the influence of friction and cohesion in some problems of statics.


Perhaps the most significant fact about this memoir from a mathematical point of view is Coulomb's use of the calculus of variations to solve engineering problems. As Gillmor writes in :-


In this one memoir of 1773 there is almost an embarrassment of riches, for Coulomb proceeded to discuss the theory of comprehensive rupture of masonry piers, the design of vaulted arches, and the theory of earth pressure. In the latter he developed a generalised sliding wedge theory of soil mechanics that remains in use today in basic engineering practice. A reason, perhaps, for the relative neglect of this portion of Coulomb's work was that he sought to demonstrate the use of variational calculus in formulating methods of approach to fundamental problems in structural mechanics rather than to give numerical solutions to specific problems.


It is often the case that a sophisticated use of mathematics in an application to an area where most have less mathematical sophistication, gives the work a long term values which is not often seen at the time. The memoir was certainly highly valued by the Académie des Sciences for it led to him being named as Bossut's correspondent on 6 July 1774. From Bouchain, Coulomb was next posted to Cherbourg. While he was there he wrote a famous memoir on the magnetic compass which he submitted for the Grand Prix of the Académie des Sciences in 1777.


This 1777 paper won Coulomb a share of the prize and it contained his first work on the torsion balance [1]:-


... his simple, elegant solution to the problem of torsion in cylinders and his use of the torsion balance in physical applications were important to numerous physicists in succeeding years. ... Coulomb developed a theory of torsion in thin silk and hair threads. Here he was the first to show how the torsion suspension could provide physicists with a method of accurately measuring extremely small forces.


Another interesting episode occurred during the time which Coulomb spent at Cherbourg. Robert-Jacques Turgot was appointed comptroller general by Louis XVI on 24 August 1774. He began to feel threatened by his political opponents in 1775 and began a series of reforms. Among these was the reform of the Corps du Génie and Turgot called for memoirs on its possible reorganisation. Coulomb submitted a memoir giving his ideas and it is a fascinating opportunity to understand his political views. Coulomb wanted the state and the individual to play equal roles. He proposed that the Corps du Génie in particular, and all public service in general, should recognise the talents of its individual members in promotion within the organisation.


In 1779 Coulomb was sent to Rochefort to collaborate with the Marquis de Montalembert in constructing a fort made entirely from wood near Ile d'Aix. Like Coulomb, the Marquis de Montalembert had a reputation as a military engineer designing fortifications, but his innovative work had been criticised by many French engineers [2]:-


Viewing fortresses as nothing more than immense permanent batteries designed to pour overwhelming fire on attacking armies, Montalembert simplified the intricate geometric designs of Vauban and relied on simple polygonal structures, often with detached peripheral forts instead of projecting bastions.


During his time at Rochefort, Coulomb carried on his research into mechanics, in particular using the shipyards in Rochefort as laboratories for his experiments. His studies into friction in Rochefort led to Coulomb's major work on friction Théorie des machines simples which won him the Grand Prix from the Académie des Sciences in 1781. In this memoir Coulomb [1]:-


... investigated both static and dynamic friction of sliding surfaces and friction in bending of cords and in rolling. From examination of many physical parameters, he developed a series of two-term equations, the first term a constant and the second term varying with time, normal force, velocity, or other parameters.


Because of this prize winning work, the authors of [5] write:-


Coulomb's contributions to the science of friction were exceptionally great. Without exaggeration, one can say that he created this science.


In fact this 1781 memoir changed Coulomb's life. He was elected to the mechanics section of the Académie des Sciences as a result of this work, and he moved to Paris where he now held a permanent post. He never again took on any engineering projects, although he did remain as a consultant on engineering matters, and he devoted his life from this point on to physics rather than engineering. He wrote seven important treatises on electricity and magnetism which he submitted to the Académie des Sciences between 1785 and 1791. These seven papers are discussed in [6] where the author shows that Coulomb:-


... had obtained some remarkable results by using the torsion balance method: law of attraction and repulsion, the electric point charges, magnetic poles, distribution of electricity on the surface of charged bodies and others. The importance of Coulomb's law for the development of electromagnetism is examined and discussed.


In these he developed a theory of attraction and repulsion between bodies of the same and opposite electrical charge. He demonstrated an inverse square law for such forces and went on to examine perfect conductors and dielectrics. He suggested that there was no perfect dielectric, proposing that every substance has a limit above which it will conduct electricity. These fundamental papers put forward the case for action at a distance between electrical charges in a similar way as Newton's theory of gravitation was based on action at a distance between masses.


These papers on electricity and magnetism, although the most important of Coulomb's work over this period, were only a small part of the work he undertook. He presented twenty-five memoirs to the Académie des Sciences between 1781 and 1806. Coulomb worked closely with Bossut, Borda, de Prony, and Laplace over this period. Remarkably he participated in the work of 310 committees of the Academy. He still was involved with engineering projects as a consultant, the most dramatic of which was his report on canal and harbour improvements in Brittany in 1783-84. He had been pressed into this task against his better judgement and he ended up taking the blame when criticisms were made and he spent a week in prison in November 1783.


He also undertook services for the respective French governments in such varied fields as education and reform of hospitals. In 1787 he made a trip to England to report on the conditions in the hospitals of London. In July 1784 he was appointed to look after the royal fountains and took charge of a large part of the water supply of Paris. On 26 February 1790 Coulomb's first son was born, although he was not married to Louise Françoise LeProust Desormeaux who was the mother of his son.


When the French Revolution began in 1789 Coulomb had been deeply involved with his scientific work. Many institutions were reorganised, not all to Coulomb's liking, and he retired from the Corps du Génie in 1791. At about the same time that the Académie des Sciences was abolished in August 1783, he was removed from his role in charge of the water supply and, in December 1793, the weights and measures committee on which he was serving was also disbanded. Coulomb and Borda retired to the country to do scientific research in a house he owned near Blois.


The Académie des Sciences was replaced by the Institut de France and Coulomb returned to Paris when he was elected to the Institute in December 1795. On 30 July 1797 his second son was born and, in 1802, he married Louise Françoise LeProust Desormeaux, the mother of his two sons. We mentioned above that Coulomb was involved with services to education. These were largely between 1802 and 1806 when he was inspector general of public instruction and, in that role, he was mainly responsible for setting up the lycées across France.


Let us end with quoting the tribute paid to him by Biot who wrote:-


It is to Borda and to Coulomb that one owes the renaissance of true physics in France, not a verbose and hypothetical physics, but that ingenious and exact physics which observes and compares all with rigour.

Johann Carl Friedrich Gauss

Johann Carl Friedrich Gauss

Born: 30 April 1777 in Brunswick, Germany

Died: 23 February 1855 in Göttingen,  Germany                                                                                                                                                                            C.F.Gauss  is one of the greatest mathematicians of all time. Gauss was born to a poorfamily. His talents were recognized at an early age. He received scholarship which helped him devote himself to research at college and later life. He rediscovered many important results at college  and in 1796 showed which regular polygons can be drawn by only ruler and compass. This was a centuries old open problem. His  Phd thesis was  about  fundamental therem of algebra. He gave  many proofs of  this  theoren during his life and clarified the notion  of complex numbers  (a+bi, where i is square root of -1 ) . Gauss made many important contributions to number theory. He formulated prime number theorem, which states that number of primes less than x is assimptotically ~x/logx. (error term is related to famous Riemann hypothesis which might have been recently proven)He published Disquisitiones Arithmeticae in 1801,  which  contained a his  proof of  quadratic reciprocity.  Quadratic reciprocity is a relation between Legendre symbols of two prime numbers.In  1807 he became director of  observatory in Göttingen. In 1809 he pusblished an  important work on  astronomy. His work on possibility of noneuclidean geometry later led to discovery of hyperbolic geometry by Bolyai, son of his friend.    He introduced gaussian gravitational constant, least squares method, normal (Gaussian ) distribution. In 1818 his work on geodesy led  to notion of curvature and he proved two surfaces are isometric if and only if  there is a map between them which preserves curvature. In his later life  (1831) he collaborated with W. Weber to do important work on electricity and magnetism. Gauss  was conservative in his views and usually worked  alone.  Most of his work  was not published  and were  rediscovered by others.  Although he didn't like teaching some of his students  also became  famous mathematicians. Gauss married twice and had seven children. 

Gauss's teacher there was Kaestner, whom Gauss often ridiculed. Gauss left Göttingen in 1798 without a diploma, but by this time he had made one of his most important discoveries - the construction of a regular 17-gon by ruler and compasses This was the most major advance in this field since the time of Greek mathematics and was published as Section VII of Gauss's famous work, Disquisitiones Arithmeticae. Gauss returned to Brunswick where he received a degree in 1799. After the Duke of Brunswick had agreed to continue Gauss's stipend, he requested that Gauss submit a doctoral dissertation to the University of Helmstedt.

Although he did not disclose his methods at the time, Gauss had used his least squares approximation method. In June 1802 Gauss visited Olbers who had discovered Pallas in March of that year and Gauss investigated its orbit. Olbers requested that Gauss be made director of the proposed new observatory in Göttingen, but no action was taken. Gauss began corresponding with Bessel, whom he did not meet until 1825, and with Sophie Germain.

In 1807 Gauss left Brunswick to take up the position of director of the Göttingen observatory. Gauss arrived in Göttingen in late 1807. In 1808 his father died, and a year later Gauss's wife Johanna died after giving birth to their second son, who was to die soon after her.

Gauss's work never seemed to suffer from his personal tragedy. He published his second book, Theoria motus corporum coelestium in sectionibus conicis Solem ambientium, in 1809, a major two volume treatise on the motion of celestial bodies. In the first volume he discussed differential equations, conic sections and elliptic orbits, while in the second volume, the main part of the work, he showed how to estimate and then to refine the estimation of a planet's orbit.

Gauss had been asked in 1818 to carry out a geodesic survey of the state of Hanover to link up with the existing Danish grid. Gauss was pleased to accept and took personal charge of the survey, making measurements during the day and reducing them at night, using his extraordinary mental capacity for calculations. He regularly wrote to Schumacher, Olbers and Bessel, reporting on his progress and discussing problems. Because of the survey, Gauss invented the heliotrope which worked by reflecting the Sun's rays using a of mirrors and a small telescope. However, inaccurate base lines were used for the survey and an unsatisfactory network of triangles.

From the early 1800s Gauss had an interest in the question of the possible existence of a non-Euclidean geometry. He discussed this topic at length with Farkas Bolyai and in his correspondence with Gerling and Schumacher. In a book review in 1816 he discussed proofs which deduced the axiom of parallels from the other Euclidean axioms, suggesting that he believed in the existence of non-Euclidean geometry, although he was rather vague.

The period 1817-1832 was a particularly distressing time for Gauss. He took in his sick mother in 1817, who stayed until her death in 1839, while he was arguing with his wife and her family about whether they should go to Berlin. He had been offered a position at Berlin University and Minna and her family were keen to move there. Gauss, however, never liked change and decided to stay in Göttingen. In 1831 Gauss's second wife died after a long illness. In 1831, Wilhelm Weber arrived in Göttingen as physics professor filling Tobias Mayer's chair. Gauss had known Weber since 1828 and supported his appointment.

In 1832, Gauss and Weber began investigating the theory of terrestrial magnetism after Alexander von Humboldt attempted to obtain Gauss's assistance in making a grid of magnetic observation points around the Earth. Gauss was excited by this prospect and by 1840 he had written three important papers on the subject: Intensitas vis magneticae terrestris ad mensuram absolutam revocata (1832), Allgemeine Theorie des Erdmagnetismus (1839) and Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungskräfte (1840).

These papers all dealt with the current theories on terrestrial magnetism, including Poisson's ideas, absolute measure for magnetic force and an empirical definition of terrestrial magnetism. Dirichlet's principle was mentioned without proof. Allgemeine Theorie... showed that there can only be two poles in the globe and went on to prove an important theorem, which concerned the determination of the intensity of the horizontal component of the magnetic force along with the angle of inclination. Gauss used the Laplace equation to aid him with his calculations, and ended up specifying a location for the magnetic South pole.

Humboldt had devised a calendar for observations of magnetic declination. However, once Gauss's new magnetic observatory (completed in 1833 - free of all magnetic metals) had been built, he proceeded to alter many of Humboldt's procedures, not pleasing Humboldt greatly. However, Gauss's changes obtained more accurate results with less effort. Gauss and Weber achieved much in their six years together. They discovered Kirchhoff's laws, as well as building a primitive telegraph device which could send messages over a distance of 5000 ft. However, this was just an enjoyable pastime for Gauss.

He was more interested in the task of establishing a world-wide net of magnetic observation points. This occupation produced many concrete results. The Magnetischer Verein and its journal were founded, and the atlas of geomagnetism was published, while Gauss and Weber's own journal in which their results were published ran from 1836 to 1841. In 1837, Weber was forced to leave Göttingen when he became involved in a political dispute and, from this time, Gauss's activity gradually decreased. He still produced letters in response to fellow scientists' discoveries usually remarking that he had known the methods for years but had never felt the need to publish. Sometimes he seemed extremely pleased with advances made by other mathematicians, particularly that of Eisenstein and of Lobachevsky.

Gauss and Weber achieved much in their six years together. They discovered Kirchhoff's laws, as well as building a primitive telegraph device which could send messages over a distance of 5000 ft. However, this was just an enjoyable pastime for Gauss. He was more interested in the task of establishing a world-wide net of magnetic observation points. This occupation produced many concrete results. The Magnetischer Verein and its journal were founded, and the atlas of geomagnetism was published, while Gauss and Weber's own journal in which their results were published ran from 1836 to 1841.

In 1837, Weber was forced to leave Göttingen when he became involved in a political dispute and, from this time, Gauss's activity gradually decreased. He still produced letters in response to fellow scientists' discoveries usually remarking that he had known the methods for years but had never felt the need to publish. Sometimes he seemed extremely pleased with advances made by other mathematicians, particularly that of Eisenstein and ofLobachevsky.

Gauss spent the years from 1845 to 1851 updating the Göttingen University widow's fund. This work gave him practical experience in financial matters, and he went on to make his fortune through shrewd investments in bonds issued by private companies.

Two of Gauss's last doctoral students were Moritz Cantor and Dedekind. Dedekind wrote a fine description of his supervisor

... usually he sat in a comfortable attitude, looking down, slightly stooped, with hands folded above his lap. He spoke quite freely, very clearly, simply and plainly: but when he wanted to emphasise a new viewpoint ... then he lifted his head, turned to one of those sitting next to him, and gazed at him with his beautiful, penetrating blue eyes during the emphatic speech. ... If he proceeded from an explanation of principles to the development of mathematical formulas, then he got up, and in a stately very upright posture he wrote on a blackboard beside him in his peculiarly beautiful handwriting: he always succeeded through economy and deliberate arrangement in making do with a rather small space. For numerical examples, on whose careful completion he placed special value, he brought along the requisite data on little slips of paper.

Gauss presented his golden jubilee lecture in 1849, fifty years after his diploma had been granted by Helmstedt University. It was appropriately a variation on his dissertation of 1799. From the mathematical community only Jacobi and Dirichlet were present, but Gauss received many messages and honours.

From 1850 onwards Gauss's work was again nearly all of a practical nature although he did approve Riemann's doctoral thesis and heard his probationary lecture. His last known scientific exchange was with Gerling. He discussed a modified Foucault pendulum in 1854. He was also able to attend the opening of the new railway link between Hanover and Göttingen, but this proved to be his last outing. His health deteriorated slowly, and Gauss died in his sleep early in the morning of 23 February, 1855.